Pith Number

pith:ZHQ7PBVZ

pith:2026:ZHQ7PBVZJYX4RNONQE72XZRHZX

not attested not anchored not stored refs pending

An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families

Xinyue Zhang, Zhiqiang Xu

arxiv:2606.28797 v1 · 2026-06-27 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZHQ7PBVZJYX4RNONQE72XZRHZX}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-06-30T01:16:52.369680Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9e1f786b94e2fc8b5cd813fabe627cddb68b15ffb4d9e4bc297a4644dfe7a91

Aliases

arxiv: 2606.28797 · arxiv_version: 2606.28797v1 · doi: 10.48550/arxiv.2606.28797 · pith_short_12: ZHQ7PBVZJYX4 · pith_short_16: ZHQ7PBVZJYX4RNON · pith_short_8: ZHQ7PBVZ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZHQ7PBVZJYX4RNONQE72XZRHZX \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c9e1f786b94e2fc8b5cd813fabe627cddb68b15ffb4d9e4bc297a4644dfe7a91

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "adabe46394b1cc0883a93553abd33a0c58dc9dc4028a6dadf9f6b2bb8844ac17",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-27T08:09:09Z",
    "title_canon_sha256": "6213ea6680274c0217676de5b75623fe3165da87d82e35adfb3fbcc489961968"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.28797",
    "kind": "arxiv",
    "version": 1
  }
}